Research interests

My mathematical expertise is in the field of nonlinear partial differential
equations. In particular, the rigorous derivation of new effective models
in various problems in natural sciences using novel mathematical techniques
is one of my major interests. In my diploma I gave a rigorous
justification of an evolutionary elastoplastic plate model for continuum
mechanics using the notion of Gamma-convergence.
In a joint work with U. Stefanelli (Vienna), we extended the Weighted-Energy-Dissipation
principle from parabolic to hyperbolic equations to make them accessible to variational methods.

In the recent years, the mathematical modeling, analysis, and simulation of optoelectronic devices, such as solar cells and organic light-emitting diodes, has become an essential application for me.
I work closely with my colleagues Annegret Glitzky, Thomas Koprucki, Jürgen Fuhrmann, and Duy-Hai Doan from WIAS on organic devices.
In a joint work with the Dresden Integrated Center for Applied Physics and Photonic Materials, in particular with Axel Fischer, Reinhard Scholz and Sebastian Reineke, we derived a novel PDE model, involving the p(x)-Laplacian
with discontinuous p(x), to describe the current and heat flow in organic light-emitting diodes. This was the first model to correctly predict S-shaped current-voltage characteristics with regions of negative differential resistance as observed in measurements.

Moreover, with Michael Sawatzki and Hans Kleemann from IAPP we investigate the behavior and new concepts of organic transistors.

However, also the more abstract theory behind partial differential equations
is in the focus of my current work. One particular highlight of a recent joint work with
Alexander Mielke (WIAS Berlin) and Giuseppe Savaré (Pavia) was the derivation and characterization of
the so-called Hellinger-Kantorovich distance,
which can be seen as a generalization of the famous Wasserstein distance to arbitrary measures.

In general, my scientific work is guided by the aim to strengthen the cooperation between analysis and its applications by inventing and further developing the mathematical foundations and techniques to make them applicable for practical questions in other sciences.

Self-heating in 2.54mm x 2.54mm OLED sample on glass substrate.
The interplay between temperature activated hopping transport and
Joule heating leads to complicated electrothermal feedback, leading to S-shaped current-voltage
characteristics with rewgions of negative differential resistance.
This behavior was studied in Matheon project SE2 in cooperation with the Dresden Integrated Center for
Applied Physics and Photonic Materials (IAPP).

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Hole density, hole current density and electrostatic potential in Vertical Organic Field-Effect Transistor for applied drain voltage and opening of gate.
This behavior was studied in Matheon project SE18 in cooperation with the Dresden Integrated Center for
Applied Physics and Photonic Materials (IAPP).